MinT - Best Known (168−72, 168, s)-Nets in Base 4

Best Known (168−72, 168, s)-Nets in Base 4

(168−72, 168, 130)-Net over F₄ — Constructive and digital

Digital (96, 168, 130)-net over F₄, using

12 times m-reduction [i] based on digital (96, 180, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 90, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(168−72, 168, 201)-Net over F₄ — Digital

Digital (96, 168, 201)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−72, 168, 3041)-Net in Base 4 — Upper bound on s

There is no (96, 168, 3042)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 141220 608260 584387 389615 300970 223963 707185 862221 612681 136478 857307 814885 404849 713346 104704 129502 134640 > 4¹⁶⁸ [i]